The parallelogram model of analogy: A is to B as C is to D, where the vector from A to B equals the vector from C to D in embedding space. King - Man + Woman = Queen. The model was celebrated, then criticized — people's actual analogy completions do not reliably follow parallelogram geometry.
Liu et al. ask whether the model is wrong or the people are unreliable. They give identical analogy problems to LLMs and humans. The LLM completions receive higher ratings and show stronger parallelogram alignment in GloVe embeddings. The model is not wrong. People are unreliable.
The source of the unreliability: humans default to accessible words. Given A:B::C:?, they reach for a D that is related to C in any way, not specifically in the way that B is related to A. The relation-preserving constraint is cognitively expensive. The frequency-based shortcut is cheap. Humans take the shortcut more often than the model predicts.
The LLM advantage disappears when comparing only the most frequent response from each system. The best human answer is as good as the best LLM answer. The difference is in consistency — the LLM produces parallelogram-aligned completions reliably, while humans produce them intermittently. The model captures the ideal that both systems can achieve but only one achieves on average.
The structural insight: the parallelogram model was validated, invalidated, and revalidated — not because the evidence changed but because the comparison class changed. Compared to the idealized model, human analogies fail. Compared to human analogies, LLM analogies succeed. The model was always correct as a description of what analogy should be. It was wrong as a description of what humans do. LLMs close the gap between the normative model and the descriptive behavior.